Polarizabilities encode the second order reaction of a body subjected to an electromagnetic field,
e.g. the reaction of a nucleon probed
by a low energy photon [1]}. The complete reaction is described by two Compton scattering amplitudes, \(f_1\)  (spin-independent)
and \(f_2\)  (spin-dependent). Considering for now real photons (\(Q^2=0\) ), one can expand \(f_1\) 
and \(f_2\)  in term of \(\nu \) :
\(f_1(\nu )=-\frac{\alpha }{M}+\big (\alpha _E+\beta _M \big )\nu ^2+\mathcal {O}(\nu ^4), \nonumber \\f_2(\nu )=-\frac{\alpha \kappa ^2}{2M^2}\nu +\gamma _0\nu ^3+\mathcal {O}(\nu ^5), \nonumber \) 
